Odds of a 20-Sided Die

[babybells96]

You are rolling a 20 side die where the sides are numbered 1 through 20. Find the indicated odds:

In favor of rolling an even number less than 10.

When I tried this problem, I got 4/16, which is simplified to 1/4, as there are 4 numbers that are even and less than 20 and 16 numbers that are not even and less than 20. But, I'm not sure about this problem.
Thank you!

 

[pka]

You are rolling a 20 side die where the sides are numbered 1 through 20. Find the indicated odds:
In favor of rolling an even number less than 10.
When I tried this problem, I got 4/16, which is simplified to 1/4, as there are 4 numbers that are even and less than 20 and 16 numbers that are not even and less than 20. But, I'm not sure about this problem.

Actually your answer is correct: \(\displaystyle \dfrac{4}{16}\).

The question asks about odds.

\(\displaystyle \text{Probability }\ne\text{ odds.}\)

The probability of getting an even number less that ten is \(\displaystyle \dfrac{4}{20}\), the favorable number divided by the total possible.

BUT ODDS are calculated as the ratio of the probability for to the probability against.
\(\displaystyle \dfrac{\frac{4}{20}}{\frac{16}{20}}=\dfrac{4}{16}\)

 

[dsk2]

A little more on the subject: http://www.math-magic.com/probability/prob_to_odds.htm

 

[babybells96]

Thank you very much for your help! I really appreciate it.

 

[lookagain]

You are rolling a 20-sided die where the sides are numbered 1 through 20. Find the indicated odds:

babybells96,

you left out that it is a fair die. And, in this case, that means each face would have
1/20 probability of coming up.